This paper proposes an analysis method of the roundoff error due to finite-wordlength decoding in fractal image coding. The proposed method can be applied to large images such as 256 256 or 512 512 images because it needs no complex matrix computation. The simplified model used here ignores the effect of decimation ratio on the roundoff error because it is negligible. As an analysis result, the proposed method gives the output error variance which consists of grey-tone scaling coefficients and an iteration number. This method is tested on various types of 12 standard images which have 256 256 size or 512 512 size with 256 grey levels. Comparisons of simulation results with analysis results are given. The results show that our analysis method is valid for the fractal image coding.

Roundoff error due to iterative computation with finite wordlength degrades the quality of decoded images in fractal image coding that employs a deterministic iterated function system. This paper presents a state-space approach to roundoff error analysis of fractal image coding for grey-scale images. The output noise variance matrix and the noise matrix are derived for the measures of error and the output noise variance is newly defined as the pixel mean of diagonal elements of the output noise matrix. A quantitative comparison of experimental roundoff error with analytical result is made for the output noise variance. The result shows that our analysis method is valid for the fractal image coding. Our analysis method is useful to design a real-time and low-cost decoding hardware with finite wordlength for fractal image coding.

This paper proposes an analysis method of scaling-factor-quantization error in fractal image coding using a state-space approach with the statistical analysis method. It is shown that the statistical analysis method is appropriate and leads to a simple result, whereas the deterministic analysis method is not appropriate and leads to a complex result for the analysis of fractal image coding. We derive the output error variance matrix for the measure of error and define the output error variance by scalar quantity as the mean of diagonal elements of the output error variance matrix. Examples are given to show that the scaling-factor-quantization error due to iterative computation with finite-wordlength scaling factors degrades the quality of decoded images. A quantitative comparison of experimental scaling-factor-quantization error with analytical result is made for the output error variance. The result shows that our analysis method is valid for the fractal image coding.